Solving the problem of biological species living together by Adomian decomposition method E. Babolian a , J. Biazar b, * a University for Teacher Education, Iran b Department of Mathematics, Faculty of Science, Guilan University, P.O. Box 1914, Rasht, Iran Abstract In this paper, we use Adomian decomposition method for solving the system of nonlinear integro-differential equations derived from considering biological species living together. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Decomposition method; Integro-differential equations; Biological species 1. Introduction Consider two separate species with numbers n 1 ðtÞ and n 2 ðtÞ at time t where first species increases and the second decreases. If they are put together, as- suming that the second species will feed on the first, there will be an increase in the rate of the second species dn 2 =dt which depends not only on the present population n 1 ðtÞ but also on all previous values of the first species. When a steady-state condition is reached between these two species, it is described by the following pair of integro-differential equations: dn 1 dt ¼ n 1 ðtÞ k 1   c 1 n 2 ðtÞ Z t tT 0 f 1 ðt  sÞn 2 ðsÞ ds ! k 1 > 0; ð1aÞ Applied Mathematics and Computation 129 (2002) 339–343 www.elsevier.com/locate/amc * Corresponding author. E-mail address: biazar@cd.gu.ac.ir (J. Biazar). 0096-3003/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0096-3003(01)00043-1